Using fsolve for solving multiple equations by using loops

Question

holistic 2018-12-17

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/436187-using-fsolve-for-solving-multiple-equations-by-using-loops

评论： Matt J 2018-12-18

I'm starting to get more deeper into equation solving with Matlab and I'm facing some problems. I have multiple equations stored in Eq (here 13, but later on there will be hundreds):

   Eq= 
   X11 + v1_3/2 + X12*v1_2 - 1
     v2_3/2 - 2*X11 + X12*v2_2 + 4
     3*X11 + v3_3/2 + X12*v3_2 + 9
   X21 + X23*v1_3 + v1_2*(X22 - 1)
 X23*v2_3 - 2*X21 + v2_2*(X22 - 2)
 3*X21 + X23*v3_3 + v3_2*(X22 + 3)
   X32*v1_2 + v1_3*(X33 - 1) + 1/2
     X32*v2_2 + v2_3*(X33 - 2) - 1
   X32*v3_2 + v3_3*(X33 + 3) + 3/2

Now, I can specify a function as input to fsolve by writing each function by hand, which works:

x0 = ones(1,13);
options = optimoptions('fsolve', 'Algorithm', 'Levenberg-Marquardt');
result = fsolve(@equations, x0, options)
   
function F = equations(x)
X11=x(1);
X12=x(2);
X21=x(3);
X22=x(4);
X23=x(5);
X32=x(6);
X33=x(7);
v1_2=x(8);
v1_3=x(9);
v2_2=x(10);
v2_3=x(11);
v3_2=x(12);
v3_3=x(13);
F(1) = X11 + v1_3/2 + X12*v1_2 - 1;
F(2) = v2_3/2 - 2*X11 + X12*v2_2 + 4;
F(3) = 3*X11 + v3_3/2 + X12*v3_2 + 9;
F(4) = X21 + X23*v1_3 + v1_2*(X22 - 1);
F(5)=X23*v2_3 - 2*X21 + v2_2*(X22 - 2);
F(6)=3*X21 + X23*v3_3 + v3_2*(X22 + 3);
F(7)= X32*v1_2 + v1_3*(X33 - 1) + 1/2;
F(8)= X32*v2_2 + v2_3*(X33 - 2) - 1;
F(9)= X32*v3_2 + v3_3*(X33 + 3) + 3/2;
end

However, I can't possibly do this for hundreds of equations, so I need to find a way to run a loop. So I thought to first extract all symbolic variables :

allVars=symvar(Eq);

and then run a loop somewhat like this:

x0 = ones(1,13);
options = optimoptions('fsolve', 'Algorithm', 'Levenberg-Marquardt');
result = fsolve(@equations, x0, options)
function F = equations(x,Eq,allVars)
    for v=1:length(allVars)
        allVars(v)=x(v);
    end
    for n=1:length(M2)
        F(n)=Eq(n);
    end
end

This does not work unfortunately. I guess it's because the equations-function needs to have only one input x so that fsolve can handle it. But then I can't assign my equations to F asf.

how could I make this work?